Finite Group DatabasebetaFinite Group Databasebeta| order | 24206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C7 |
| direct product | C13×C7⋊D133 |
| unambiguous semidirect product | C7⋊(C13×D133) |
| unambiguous semidirect product | C19⋊(C13×C7⋊D7) |
| Fitting, socle, Hall | C72×C13×C19 ⋊ C2 |
| derived, Hall | C72×C19 ⋊ C2×C13 |
| Hall | C72×C13 ⋊ D19 |
| Hall | C13×C19 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C13×D19 |
| Sylow | C19 ⋊ C13×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C7⋊D133 |
| commutator, cosocle, hypocenter | C72×C19 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C72×C13×C19 | C2 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C13 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12103 |
6071 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24206, 18);